{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 6. Kernel Methods"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "from prml.kernel import (\n",
    "    PolynomialKernel,\n",
    "    RBF,\n",
    "    GaussianProcessClassifier,\n",
    "    GaussianProcessRegressor\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def create_toy_data(func, n=10, std=1., domain=[0., 1.]):\n",
    "    x = np.linspace(domain[0], domain[1], n)\n",
    "    t = func(x) + np.random.normal(scale=std, size=n)\n",
    "    return x, t\n",
    "\n",
    "def sinusoidal(x):\n",
    "        return np.sin(2 * np.pi * x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 6.1 Dual Representation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_train, y_train = create_toy_data(sinusoidal, n=10, std=0.1)\n",
    "x = np.linspace(0, 1, 100)\n",
    "\n",
    "model = GaussianProcessRegressor(kernel=PolynomialKernel(3, 1.), beta=int(1e10))\n",
    "model.fit(x_train, y_train)\n",
    "\n",
    "y = model.predict(x)\n",
    "plt.scatter(x_train, y_train, facecolor=\"none\", edgecolor=\"b\", color=\"blue\", label=\"training\")\n",
    "plt.plot(x, sinusoidal(x), color=\"g\", label=\"sin$(2\\pi x)$\")\n",
    "plt.plot(x, y, color=\"r\", label=\"gpr\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 6.4 Gaussian Processes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 6.4.2 Gaussian processes for regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_train, y_train = create_toy_data(sinusoidal, n=7, std=0.1, domain=[0., 0.7])\n",
    "x = np.linspace(0, 1, 100)\n",
    "\n",
    "model = GaussianProcessRegressor(kernel=RBF(np.array([1., 15.])), beta=100)\n",
    "model.fit(x_train, y_train)\n",
    "\n",
    "y, y_std = model.predict(x, with_error=True)\n",
    "plt.scatter(x_train, y_train, facecolor=\"none\", edgecolor=\"b\", color=\"blue\", label=\"training\")\n",
    "plt.plot(x, sinusoidal(x), color=\"g\", label=\"sin$(2\\pi x)$\")\n",
    "plt.plot(x, y, color=\"r\", label=\"gpr\")\n",
    "plt.fill_between(x, y - y_std, y + y_std, alpha=0.5, color=\"pink\", label=\"std\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 6.4.3 Learning the hyperparameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_train, y_train = create_toy_data(sinusoidal, n=7, std=0.1, domain=[0., 0.7])\n",
    "x = np.linspace(0, 1, 100)\n",
    "\n",
    "plt.figure(figsize=(20, 5))\n",
    "plt.subplot(1, 2, 1)\n",
    "model = GaussianProcessRegressor(kernel=RBF(np.array([1., 1.])), beta=100)\n",
    "model.fit(x_train, y_train)\n",
    "y, y_std = model.predict(x, with_error=True)\n",
    "plt.scatter(x_train, y_train, facecolor=\"none\", edgecolor=\"b\", color=\"blue\", label=\"training\")\n",
    "plt.plot(x, sinusoidal(x), color=\"g\", label=\"sin$(2\\pi x)$\")\n",
    "plt.plot(x, y, color=\"r\", label=\"gpr {}\".format(model.kernel.params))\n",
    "plt.fill_between(x, y - y_std, y + y_std, alpha=0.5, color=\"pink\", label=\"std\")\n",
    "plt.legend()\n",
    "\n",
    "plt.subplot(1, 2, 2)\n",
    "model.fit(x_train, y_train, iter_max=100)\n",
    "y, y_std = model.predict(x, with_error=True)\n",
    "plt.scatter(x_train, y_train, facecolor=\"none\", edgecolor=\"b\", color=\"blue\", label=\"training\")\n",
    "plt.plot(x, sinusoidal(x), color=\"g\", label=\"sin$(2\\pi x)$\")\n",
    "plt.plot(x, y, color=\"r\", label=\"gpr {}\".format(np.round(model.kernel.params, 2)))\n",
    "plt.fill_between(x, y - y_std, y + y_std, alpha=0.5, color=\"pink\", label=\"std\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 6.4.4 Automatic relevance determination"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def create_toy_data_3d(func, n=10, std=1.):\n",
    "    x0 = np.linspace(0, 1, n)\n",
    "    x1 = x0 + np.random.normal(scale=std, size=n)\n",
    "    x2 = np.random.normal(scale=std, size=n)\n",
    "    t = func(x0) + np.random.normal(scale=std, size=n)\n",
    "    return np.vstack((x0, x1, x2)).T, t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_train, y_train = create_toy_data_3d(sinusoidal, n=20, std=0.1)\n",
    "x0 = np.linspace(0, 1, 100)\n",
    "x1 = x0 + np.random.normal(scale=0.1, size=100)\n",
    "x2 = np.random.normal(scale=0.1, size=100)\n",
    "x = np.vstack((x0, x1, x2)).T\n",
    "\n",
    "model = GaussianProcessRegressor(kernel=RBF(np.array([1., 1., 1., 1.])), beta=100)\n",
    "model.fit(x_train, y_train)\n",
    "y, y_std = model.predict(x, with_error=True)\n",
    "plt.figure(figsize=(20, 5))\n",
    "plt.subplot(1, 2, 1)\n",
    "plt.scatter(x_train[:, 0], y_train, facecolor=\"none\", edgecolor=\"b\", label=\"training\")\n",
    "plt.plot(x[:, 0], sinusoidal(x[:, 0]), color=\"g\", label=\"$\\sin(2\\pi x)$\")\n",
    "plt.plot(x[:, 0], y, color=\"r\", label=\"gpr {}\".format(model.kernel.params))\n",
    "plt.fill_between(x[:, 0], y - y_std, y + y_std, color=\"pink\", alpha=0.5, label=\"gpr std.\")\n",
    "plt.legend()\n",
    "plt.ylim(-1.5, 1.5)\n",
    "\n",
    "model.fit(x_train, y_train, iter_max=100, learning_rate=0.001)\n",
    "y, y_std = model.predict(x, with_error=True)\n",
    "plt.subplot(1, 2, 2)\n",
    "plt.scatter(x_train[:, 0], y_train, facecolor=\"none\", edgecolor=\"b\", label=\"training\")\n",
    "plt.plot(x[:, 0], sinusoidal(x[:, 0]), color=\"g\", label=\"$\\sin(2\\pi x)$\")\n",
    "plt.plot(x[:, 0], y, color=\"r\", label=\"gpr {}\".format(np.round(model.kernel.params, 2)))\n",
    "plt.fill_between(x[:, 0], y - y_std, y + y_std, color=\"pink\", alpha=0.2, label=\"gpr std.\")\n",
    "plt.legend()\n",
    "plt.ylim(-1.5, 1.5)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### 6.4.5 Gaussian processes for classification"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def create_toy_data():\n",
    "    x0 = np.random.normal(size=50).reshape(-1, 2)\n",
    "    x1 = np.random.normal(size=50).reshape(-1, 2) + 2.\n",
    "    return np.concatenate([x0, x1]), np.concatenate([np.zeros(25), np.ones(25)]).astype(np.int)[:, None]\n",
    "\n",
    "x_train, y_train = create_toy_data()\n",
    "x0, x1 = np.meshgrid(np.linspace(-4, 6, 100), np.linspace(-4, 6, 100))\n",
    "x = np.array([x0, x1]).reshape(2, -1).T\n",
    "\n",
    "model = GaussianProcessClassifier(RBF(np.array([1., 7., 7.])))\n",
    "model.fit(x_train, y_train)\n",
    "y = model.predict(x)\n",
    "\n",
    "plt.scatter(x_train[:, 0], x_train[:, 1], c=y_train.ravel())\n",
    "plt.contourf(x0, x1, y.reshape(100, 100), levels=np.linspace(0,1,3), alpha=0.2)\n",
    "plt.colorbar()\n",
    "plt.xlim(-4, 6)\n",
    "plt.ylim(-4, 6)\n",
    "plt.gca().set_aspect('equal', adjustable='box')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
